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equatorial coordinate system

 
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equatorial coordinate system

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equatorial coordinate system, the most commonly used astronomical coordinate system for indicating the positions of stars or other celestial objects on the celestial sphere. The celestial sphere is an imaginary sphere with the observer at its center. It represents the entire sky; all celestial objects other than the earth are imagined as being located on its inside surface. If the earth's axis is extended, the points where it intersects the celestial sphere are called the celestial poles; the north celestial pole is directly above the earth's North Pole, and the south celestial pole directly above the earth's South Pole. The great circle on the celestial sphere halfway between the celestial poles is called the celestial equator; it can be thought of as the earth's equator projected onto the celestial sphere. It divides the celestial sphere into the northern and southern skies. An important reference point on the celestial equator is the vernal equinox, the point at which the sun crosses the celestial equator in March.

To designate the position of a star, the astronomer considers an imaginary great circle passing through the celestial poles and through the star in question. This is the star's hour circle, analogous to a meridian of longitude on earth. The astronomer then measures the angle between the vernal equinox and the point where the hour circle intersects the celestial equator. This angle is called the star's right ascension and is measured in hours, minutes, and seconds rather than in the more familiar degrees, minutes, and seconds. (There are 360 degrees or 24 hours in a full circle.) The right ascension is always measured eastward from the vernal equinox. Next the observer measures along the star's hour circle the angle between the celestial equator and the position of the star. This angle is called the declination of the star and is measured in degrees, minutes, and seconds north or south of the celestial equator, analogous to latitude on the earth. Right ascension and declination together determine the location of a star on the celestial sphere. The right ascensions and declinations of many stars are listed in various reference tables published for astronomers and navigators. Because a star's position may change slightly (see proper motion and precession of the equinoxes), such tables must be revised at regular intervals. By definition, the vernal equinox is located at right ascension 0h and declination 0°.

Another useful reference point is the sigma point, the point where the observer's celestial meridian intersects the celestial equator. The right ascension of the sigma point is equal to the observer's local sidereal time. The angular distance from the sigma point to a star's hour circle is called its hour angle; it is equal to the star's right ascension minus the local sidereal time. Because the vernal equinox is not always visible in the night sky (especially in the spring), whereas the sigma point is always visible, the hour angle is used in actually locating a body in the sky.

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Equatorial coordinate system

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Equatorial coordinate system (celestial).svg

The equatorial coordinate system is a widely-used method of mapping celestial objects. It functions by projecting the Earth's geographic poles and equator onto the celestial sphere. The projection of the Earth's equator onto the celestial sphere is called the celestial equator. Similarly, the projections of the Earth's north and south geographic poles become the north and south celestial poles, respectively.

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Use in astronomy

The equatorial coordinate system allows all earthbound observers to describe the apparent location in the sky of sufficiently distant objects using the same pair of numbers: the right ascension and declination. For example, a given star has roughly constant equatorial coordinates. In contrast, in the horizontal coordinate system, a star's position in the sky is different based on the geographical latitude and longitude of the observer, and is constantly changing based on the time of day.

The equatorial coordinate system is commonly used by telescopes equipped with equatorial mounts by employing setting circles. Setting circles in conjunction with a star chart or ephemeris allow a telescope to be easily pointed at known objects on the celestial sphere.

Over long periods of time, precession and nutation effects alter the Earth's orbit and thus the apparent location of the stars. Likewise, proper motion of the stars themselves will affect their coordinates as seen from Earth. When considering observations separated by long intervals, it is necessary to specify an epoch (frequently J2000.0, for older data B1950.0) when specifying coordinates of planets, stars, galaxies, etc.

Left A star is at culmination on an observer's meridian (HA = 0 h), then RA = LST. Right Now the vernal equinox point is at culmination on the meridian m (LST = 0 h) (Positive angles: RA, counterclockwise; HA and LST, clockwise)

Declination

Main article: Declination

The latitudinal angle of the equatorial system is called declination (Dec for short). It measures the angle of an object above or below the celestial equator.[1][2] Objects in the northern celestial hemisphere have a positive declination, and those in the southern celestial hemisphere have a negative declination. For example, the north celestial pole has a declination of +90°.

Right ascension

Main article: Right ascension

The longitudinal angle is called the right ascension (RA for short). It measures the angle of an object east of the apparent location of the center of the Sun at the moment of the March equinox, a position known as the vernal equinox point or the first point of Aries.[1] The vernal equinox point is one of the two points where the ecliptic intersects with the celestial equator. Unlike geographic longitude, right ascension is usually measured in sidereal hours instead of degrees, because an apparent rotation of the equatorial coordinate system takes 24 hours of sidereal time to complete. There are (360 degrees / 24 hours) = 15 degrees in one hour of right ascension.

Hour angle

Main article: Hour angle

When calculating geography-dependent phenomena such as sunrise or moonrise, right ascension may be converted into hour angle as an intermediate step.[3] A celestial object's hour angle is measured relative to the observer's location on the Earth; a star on the observer's celestial meridian at a given moment in time is said to have a zero hour angle. One sidereal hour later (approximately 0.997269583 solar hours later), the Earth's rotation will make that star appear to the west of the meridian, and that star's hour angle will be +1 sidereal hour.

GEI Coordinates

There are a number of cartesian variants of equatorial coordinates. The most common of these is called the geocentric equatorial inertial (GEI) coordinate system.

  • GEI coordinates have the z-axis pointing along the axis of rotation of the earth (north positive), the x-axis pointing in the direction of the Sun during the vernal equinox and the y-axis defined as the cross product of z and x (in that order) to create a right-handed coordinate system. Like the polar variants described above, the direction of the x-axis drifts due to orbital precession and thus an epoch must be specified.
  • In this context, J2000.0 can also refer not just to the Julian 2000 Epoch, but also to the entire GEI coordinate frame at that epoch.
  • GEI systems are also sometimes "True of Date". This means that the epoch at the exact moment at which the data is collected is used as the epoch of the coordinate system.
  • The direction of the x-axis is also described as the first point of the constellation Aries.
  • This system is often used for describing the state vectors of spacecraft as well as various phenomena in space physics.[4][5][6]

See also

References

  1. ^ a b Peter Duffett-Smith. Practical Astronomy with Your Calculator, third edition. Cambridge University Press. pp. 28–29. ISBN 0521356997. 
  2. ^ Meir H. Degani (1976). Astronomy Made Simple. Doubleday & Company, Inc. p. 216. ISBN 0-385-08854-X. 
  3. ^ Peter Duffett-Smith. Practical Astronomy with Your Calculator, third edition. Cambridge University Press. pp. 34–36. ISBN 0521356997. 
  4. ^ Geocentric coordinate systems, http://sspg1.bnsc.rl.ac.uk/Share/Coordinates/geo_sys.htm 
  5. ^ Space physics coordinate systems, http://www.iki.rssi.ru/vprokhor/coords.htm 
  6. ^ Christopher T. Russell, Geophysical Coordinate Transformations, http://dawn.ucla.edu/personnel/russell/papers/gct1.html/ 

This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)

 
 

 

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